So if all living
Europeans have a common ancestor who lived around the year 1400,
what happens when you look further back into the past?

Chang's
calculations suggest that about one fifth of Europeans who lived a
millennium ago have no living ancestors today.

This seems to be
because their ancestral line died off along the way.

Conversely, as
Rutherford writes, the implication is that everyone else alive
a millennium ago is related to Europeans alive today.

"One way to think of it is
to accept that everyone of European descent should have billions
of ancestors at a time in the tenth century, but there weren't
billions of people around then, so try to cram them into the
number of people that actually were.

The math that
falls out of that apparent impasse is that all of the billions
of lines of ancestry have coalesced into not just a small number
of people, but effectively literally everyone who was alive at
that time."

Chang's complex
mathematical paper concludes with a passage that's rather poetic for
a numbers guy:

"Our findings
suggest a remarkable proposition:

no matter the languages we
speak or the color of our skin, we share ancestors who planted
rice on the banks of the Yangtze, who first domesticated horses
on the steppes of the Ukraine, who hunted giant sloths in the
forests of North and South America, and who labored to build the
Great Pyramid of Khufu."

Still, mapping out
an exact pedigree for an individual is exceedingly difficult.

For instance, the
"family trees" that Ancestry.com
provides its users only go back up to 10 generations - sometimes
less if users want more reliable results.

Often someone's
luck with tracing their family lineage comes down to whether or not
they can find documents that detail the lives of their ancestors.

At a certain point,
the act of tracing family lineage becomes purely theoretical, as Mark
Humphrys, a computer scientist at Dublin City University, told
Steve Olson in an
article for
The Atlantic:

"You can ask
whether everyone in the Western world is descended from
Charlemagne, and the answer is yes, we're all descended from
Charlemagne.